The Skeleton of the Amoeba
A new field has recently emerged in which mathematicians modify geometric objects so much that only a "skeleton" of the actual shape remains. However, the structures retain many of their original properties - revealing unexpected mysteries.
When trying to solve a complicated math problem, sometimes the direct way proves difficult. In these cases it is worth deviating from the usual path and taking a detour.
In such a situation was Gerolamo Cardano in the 16th century. At that time, he had a hard time solving cubic equations. But at some point he had a brilliant idea that would shape modern mathematics in an unexpected way: During his calculations, he introduced roots from negative numbers - today they are known as imaginary numbers. He didn't attach any special importance to them, but they helped him to solve the tricky tasks. In the meantime, complex numbers, which are composed of real and imaginary numbers, have turned out to be so important that many current advances in the natural sciences would be unthinkable without them.
Tropical geometry is another example of a useful detour. It emerged in the 1980s and has since grown into an active field of research that also influences other areas of mathematics. One of the biggest beneficiaries of this development is algebraic geometry. In this area, as mathematicians have discovered, it can be worthwhile to deviate from tropical geometry…
